Portfolio Adjustments: An Application to Rural Banking

A general method is provided for evaluating how an expected-utility-maximizing choice is changed in response to factors shifting the mean-variance (EV) efficient set and changes in the decision maker's level of risk aversion. Substitution and income effects under uncertainty are defined, related to those existing under certainty, and analyzed graphically and in a quadratic programming model of a rural bank. The bank application includes risk and liquidity components and indicates that the magnitude of the portfolio response may not be trivial. Evidence is also provided indicating the consistency between bank behavior and the EV decision criterion. Key words: expected utility, portfolio theory, risk, rural banking. Numerous studies in decision making under risk have focused primarily on generating in-formation needed to identify an initial expected-utility-maximizing choice from a mean-variance (EV) efficient set. Such studies have sought better ways to order portfolios into efficient and inefficient sets and better ways to measure probability distributions and utility functions (Dillon). However, much less attention has been given to evaluating the re-sponse of the expected-utility-maximizing choice to changes in decision parameters that shift the EV set (Tobin, Cass and Stiglitz, Levy, Adler, Royama and Hamada). Because this response may be significant, there is a need to develop a conceptual framework and empirical methods for predicting equilibrium adjustments under uncertainty. This paper provides a general method for evaluating how an expected-utility-maximiz-ing choice is changed in response to factors shifting the E V set and changes in the decision maker's level of risk aversion. The following sections define appropriate measures of risk aversion and shifts in the E V set caused by changes in the probability distribution of re-turns on risky assets, changes in returns on safe assets, and changes in initial wealth. Th